An unrelated parallel machine scheduling problem with past-sequence-dependent setup time and learning effects

In this paper, we study an unrelated parallel machine scheduling problem simultaneously with learning effect and setup time. The setup time is proportional to the length of the already processed jobs. That is, the setup time of each job is past-sequence-dependent. The objective is to minimize the total absolute deviation of job completion times. We show that the proposed problem is polynomially solvable.